Mathematical model for continuous and intermittent microwave-assisted extraction of bioactive compound from plant material: Extraction of β-carotene from carrot peels

Chemical Engineering Science 116 (2014) 442–451

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Mathematical model for continuous and intermittent microwave-assisted extraction of bioactive compound from plant material: Extraction of β-carotene from carrot peels Nakarin Chumnanpaisont a, Chalida Niamnuy b, Sakamon Devahastin c,n a Department of Chemical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, 126 Pracha u-tid Road, Tungkru, Bangkok 10140, Thailand b Center of Advanced Studies in Industrial Technology, Department of Chemical Engineering, Faculty of Engineering, Kasetsart University, 50 Ngam Wong Wan Road, Chatuchak, Bangkok 10900, Thailand c Department of Food Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, 126 Pracha u-tid Road, Tungkru, Bangkok 10140, Thailand

H I G H L I G H T S








Model that can be used to describe full transport phenomena during MAE is proposed. Model consists of Maxwell’s energy and species balance equations. Carrot peels were used as test material and β-carotene concentration was estimated. Model could predict temperature and β-carotene concentration evolutions adequately. Temperature prediction was compromised when solvent evaporation existed.

art ic l e i nf o

a b s t r a c t

Article history: Received 26 August 2013 Received in revised form 5 May 2014 Accepted 9 May 2014 Available online 24 May 2014

Microwave-assisted extraction (MAE) is a method that uses microwave energy to extract compounds from materials. Although many studies have recently been published on various aspects of MAE, an adequate model that can be used to predict the transport phenomena during MAE is still lacking. This study was therefore aimed to develop a mathematical model that can be used to describe the evolutions of temperature and concentration of an extract during both continuous and intermittent MAE; carrot peels were used as a test material and β-carotene concentration was modeled. The model consisting of the Maxwell’s, energy and species balance equations, along with appropriate initial and boundary conditions, was simulated using the finite element method via COMSOL MultiphysicsTM software. The model was validated by comparing the simulated results with the evolutions of the experimental temperature and β-carotene concentration. In general, the model was capable of predicting the evolutions of the temperature and β-carotene concentration quite adequately. In some cases, however, the temperature prediction was compromised due to the evaporation of solvent, which was not considered in the model. The empirical constants of the model were noted to depend on the specific absorbed microwave power and the sample-to-solvent ratio. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Extraction Food processing Mathematical modeling Simulation Transport processes

1. Introduction Solid–liquid extraction is a simple separation method that has been widely used to extract compounds from materials. There are a number of methods that can be used for such a purpose such as

n

Corresponding author. Tel.: þ 66 2 470 9244; fax: þ 66 2 470 9240. E-mail address: [email protected] (S. Devahastin).

http://dx.doi.org/10.1016/j.ces.2014.05.010 0009-2509/& 2014 Elsevier Ltd. All rights reserved.

reflux extraction, Soxhlet extraction and supercritical fluid extraction. However, these methods are either time- and solvent-consuming or too expensive for small-scale implementation (Bagherian et al., 2011; Wang et al., 2010; Amarni and Kadi, 2010). Therefore, alternative methods of extraction have been proposed to alleviate these problems. Microwave-assisted extraction (MAE) is an alternative process that uses microwave energy to extract compounds from materials. MAE has recently received much attention due to its many

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

advantages, e.g., shorter extraction time and lower solvent requirement. The fact that MAE involves volumetric heating and is a rather controllable process also makes it an attractive alternative for extraction, especially when dealing with the extraction of heat-sensitive bioactive compounds from plant materials where rapid heating and hence shorter extraction time is desired (Hiranvarachat et al., 2013; Maran et al., 2014). In order to improve the performance of MAE, it is important to first understand the basic phenomena and the effects of relevant parameters on the MAE process (Kiss et al., 2000; Pan et al., 2003; Fulzele and Satdive, 2005; Wang et al. 2006; Hemwimon et al., 2007; Spigno and De Faveri, 2009). Although there are a number of studies that investigated the use of MAE in various applications, studies on the use of mathematical models, which are important to investigate the effects of various relevant parameters on both the phenomenological behavior and performance of the process, are still quite limited. Among the available studies, Navarrete et al. (2012) modeled solvent-free microwave extraction (SFME) of essential oils from Lavandin super. The model included an interaction between electromagnetic energy and material through the use of Maxwell’s equations coupled with the differential heat and mass balance equations. The temperature evolution of the extract during SFME was simulated, but while the model could predict the amount of evaporated water containing the essential oils, it could not predict the evolution of the essential oils concentration itself. This is because the mass conservation equation for the essential oils was not presented. Later, Sinha et al. (2013) modeled MAE of yellow-red natural dye from seeds of Bixa orellana (annatto) by using the response surface methodology (RSM) and artificial neural network (ANN). The investigated variables were the solvent pH, extraction time and amount of annatto seeds used for the extraction. ANN model was noted to have a higher predictive capability than the RSM model. However, since the objective of the work was to test the effects of process parameters on the extraction efficiency, the transport phenomena (or kinetics of heat and mass transfer) during MAE were not explained. More recently, Chan et al. (2013) modeled MAE of antioxidant compounds from cocoa (Theobroma cacao L.) leaves using the adapted film theory with absorbed microwave energy as the modeling basis; it is important to note that the original film theory cannot be used to predict the extraction behavior as the model’s parameters can only be determined by fitting with the experimental extraction curves. The studied variables were the microwave power and amount of solvent loading. The model could adequately predict the extract concentration evolution with R2 values greater than 0.87. However, the model was not aimed to describe the microwave heating phenomenon. It is therefore clear that a model capable of predicting the simultaneous changes of heat (temperature) and mass (concentration of an extract) during MAE is needed. The aim of this study was to develop a mathematical model that could be used to describe the transport behavior of a material undergoing MAE; plant material was of focus here as it is a source of phytochemicals, which have received much interest from the various industries as potential alternatives to synthetic drugs and chemicals. The model consists of heat and mass balance equations along with the use of Maxwell’s equations to describe the electromagnetic field generated through the application of microwaves. Governing equations as well as the initial and boundary conditions were solved numerically using the finite element method through the use of COMSOL MultiphysicsTM software (version 3.5). Experimental data on MAE of β-carotene from carrot peels, which are a by-product from carrot processing industry that still nevertheless contains many beneficial phytochemicals, especially β-carotene and other carotenoids, were used to obtain the values of the model parameters and to validate the model.

443

Subsequently, the model was used to study intermittent MAE as a means to enhance the efficiency of the MAE process. Intermittent operation was proposed since it was expected to lead to less thermal degradation of a heat-sensitive extract; this is possible through the intermittent supply of the microwave energy, which should expectedly lead to less exposure to the high-temperature environment by the extract.

2. Experimental setup, materials and methods 2.1. Experimental setup A schematic diagram of the overall experimental setup is shown in Fig. 1. A domestic microwave oven (Samsung, GE-872D, Port Klang, Malaysia) with the inside dimensions of 30  30  19 cm was modified for MAE experiments. During modeling, however, symmetry was assumed to exist and only half of the oven was considered; therefore, the simulated dimensions were 15  30  19 cm. The oven is capable of operating at a maximum input power of 850 W at a frequency of 2450 MHz. The waveguide has the dimensions of 5  8  4.5 cm. A 1000-mL round-bottom flask containing a solvent and a sample was placed inside the microwave oven cavity at its center. The flask was fitted with an external condenser to condense the vaporized solvent, which was then collected in a graduated cylinder. Cold water ( 4 1C) was used as the condensing medium. The temperature evolution of a mixture of a sample and a solvent during MAE was measured via the use of a fiber-optic thermometer (Luxtron, m600, Santa Clara, CA); the temperature evolution data were collected at 5-s interval. 2.2. Materials Fresh carrots (Daucus carota var. sativa) was purchased from a local market and stored at 4 1C. Care was exercised to obtain fresh carrots of similar maturity from the same supplier. The possible variability of the β-carotene content of the carrots was taken into account through the reported standard deviations of the experimental data. Before starting of each experiment, carrots were washed with tap water and the excess water was removed. Carrots were then peeled; only the peels were used in this study. The peels were blanched in boiling water for 3 min to inactivate polyphenol oxidase (PPO) and peroxidase (POD) and also to modify the

Fig. 1. Modified multimode domestic microwave oven. (1) domestic microwave oven; (2) round-bottom flask; (3) external condenser; and (4) graduated cylinder.

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cellular structure to enhance the extraction as recommended by Hiranvarachat et al. (2013). β-carotene standard was purchased from Fluka Production GmbH (Buchs, Switzerland). 2.3. Methods The extraction solvent was that recommended by Hiranvarachat et al. (2013). The solvent consisted of 50% (v/v) hexane, 25% (v/v) acetone and 25% (v/v) ethanol. The boiling point of the chosen extraction solvent system was measured to be around 58 1C. The extraction procedure was that of Hiranvarachat and Devahastin (2014). In the case of the continuous MAE, two g of the peels was first ground for 1 min using a blender (Moulinex, DPA 2, Écully, France). The extraction solvent was mixed with the ground peels in the round-bottom flask. The solvent-to-sample ratio was either 75 mL:2 g or 150 mL:2 g. The mixture was then extracted under microwave irradiation. Some of the solvent evaporated and condensed after passing through the external condenser, while the carotenoids mostly remained in the solvent in the flask. After MAE the condensed solvent was mixed with the remaining extract in the flask; the flask was rinsed twice more with 25 mL of the extraction solvent to cleanse the remaining extract that might stay on the flask wall. The whole content was diluted with 30 mL of distilled water and filtered through Whatman No. 1 filter paper. A separation funnel was used to enhance the separation between the aqueous and organic phases. The organic phase, containing β-carotene, was stored in a dark tube at 4 1C prior to further analysis within 2 h. The tested input (set) microwave powers were 180 and 300 W. The former value was selected based on the study of Hiranvarachat et al. (2013) who mentioned that the optimum MAE condition for carrots was the use of 180 W microwave power and the solvent-to-sample ratio of 75 mL:2 g. However, to accelerate the extraction process, the microwave power of 300 W and the solvent-to-sample ratio of 150 mL:2 g were also tested. In each experiment, the MAE process was carried out up to a predetermined sampling time; that particular experiment was terminated at that time. A new experimental run was then performed up to the next predetermined sampling time. These steps were repeated until a complete extraction was obtained. In the case of the intermittent MAE, an ‘on’ period refers to the extraction procedures mentioned above. On the other hand, an ‘off’ period refers to the turning off of the microwave irradiation. To prolong the extraction time, two ‘on’ periods (and one ‘off’ period in between) were employed (Hiranvarachat and Devahastin, 2014). The overall experimental conditions are listed in Table 1. All experiments were performed in duplicate.

consists of Waters Alliance 2695 HPLC equipped with Waters 2998 photodiode array detector (Waters, Milford, MA). A mixture of methanol and methyl tert-butyl ether (MTBE) (75:25) was used as a mobile phase at a flow rate of 2 mL/min. Symmetrys C30 5 μm (4.6  250 mm) HPLC column (YMC, Kyoto, Japan) was used for the analysis of β-carotene. Prior to injection into the HPLC column, an extract was filtered through 0.2-μm filter. Detection of β-carotene was made at a wavelength of 450 nm. The mobile phase was degassed using an ultrasonic generator. Quantification of β-carotene was carried out based on a β-carotene standard curve, which was prepared daily by injecting β-carotene standard into the extraction solvent at six concentrations (0, 2, 4, 6, 8 and 10 μg/mL). The standard curve showed good linearity (R2 40.99).

3. Mathematical model To simplify the problem, the following assumptions were first made: initial temperature and β-carotene concentration in the extraction solvent were uniform; the amount of carrot peels was much less than that of the solvent, resulting in negligible absorption of the microwave energy and hence was not considered in the governing conservation equations; volume and phase change of the extraction solvent during MW irradiation were negligible; convection was not considered in the energy and species balance equations; mass diffusion was not considered in the species balance equation, i.e., the β-carotene concentration was assumed to be uniform throughout the whole flask; microwave oven cavity and waveguide walls were assumed to be perfectly conducting surfaces; air and flask were not heated by microwave energy because they are perfectly transparent media; the thickness of the flask was negligible, resulting in the inner and outer surfaces having the same temperature. Symmetry was assumed to exist in the extraction system. The physical model of the simulated MAE system is shown in Fig. 2.

MW oven cavity

Waveguide

2.4. β-carotene analysis

Flask containing sample + extraction solvent

Quantification of β-carotene was carried out based on the method of Hiranvarachat et al. (2013). The utilized analysis system

Fig. 2. Schematic diagram of the simulated MAE system.

Table 1 MAE conditions used to validate the mathematical model. Condition

Scheme

Solvent volume (mL)

Set MW power (W)

On period:off period:on period (min:min:min)

Total extraction time (min)

Number of times MAE was stoppeda (times)

1 2 3 4 5 6 7 8

Continuous Continuous Continuous Continuous Intermittent Intermittent Intermittent Intermittent

75 150 75 150 75 150 75 150

180 180 300 300 180 180 300 300

– – – – 3.5:10.5:3.5 6.5:19.5:6.5 1.5:4.5:1.5 2.5:7.5:2.5

7 9 5 5 17.5 32.5 7.5 12.5

5 5 4 4 6 7 6 7

a

Number of times MAE process was stopped to analyze the β-carotene concentration.

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3.2. Energy and species balance equations

3.1. Maxwell’s equations Maxwell’s equations were used to describe the electromagnetic field. The equations for the description of the magnetic and electric fields are as follows (Jian et al., 2010; Navarrete et al., 2012; Chandrasekaran et al., 2013): ,

,

∇E¼  ,

∂B ∂t

,

∇H ¼Jþ

ð1Þ ,

∂D ∂t

ð2Þ

,

∇UD ¼ q

ð3Þ

,

∇UB ¼ 0

ð4Þ

The constitutive relations between E, H, J, D and B are (Jian et al., 2010; Navarrete et al., 2012): ,

,

J ¼ sE

ð5Þ

,

,

,

,

D ¼ ε0 εr E

ð6Þ

B ¼ μ0 μr H

ð7Þ

The electric conductivity and the relative permittivity can be written as (Pozar, 2005, Jian et al., 2010; Navarrete et al., 2012):

s ¼ 2πf tan δ

ð8Þ

εr ¼ ε0 þ jε″

ð9Þ

Rearrangement of Eqs. (1)–(6) yields the following equations that can be solved for the electric field (Pozar, 2005; Jian et al., 2010):
 , js , 2 E ¼0 ð10Þ ∇ðμr 1 ∇  E Þ  k0 εr  ωε0 pffiffiffiffiffiffiffiffiffiffi k0 ¼ ω μ0 ε0

ð11Þ

The initial and boundary conditions are as follows: Initial conditions: At t ¼ 0

H¼0

and

E¼0

ð12Þ

The energy equation is written as: ρC p

∂T ¼ ∇ U ðk∇TÞ þ q‴ ∂t

and

nE ¼ 0

ð13Þ

The volumetric heat generation rate can be calculated from the electric field as:  1 q‴ ¼ ωε0 ε″Ej2 2

nðH 2 H 1 Þ ¼ 0

and

nðE2  E1 Þ ¼ 0

ð14Þ

A rectangular waveguide (TE10 mode), which is designed to transmit maximum possible power from the magnetron to the cavity, was assumed (Geedipalli et al., 2008). Poynting vector (W/m2) was used to represent the power flux associated with the propagating wave as: R S¼

,

,

where C β is the β-carotene concentration, C βmax is the maximum concentration of β-carotene, which was obtained from Soxhlet extraction experiments (Hiranvarachat et al., 2013), T d is the degradation temperature of β-carotene, which is 55 1C (Goula and Adamopoulos, 2010). This equation implies that the extraction (generation) of β-carotene took place at temperatures lower than T d . On the other hand, degradation of β-carotene took place at temperatures higher than T d . The above equations were solved numerically subjected to the following initial and boundary conditions. Initial conditions: ð21Þ

Boundary conditions: At interface between solvent and glass ð22Þ

where T 1 is the ambient temperature, which was assumed to be 25 1C and h is the convective heat transfer coefficient, which in this case represents the loss of heat from the extraction flask to the environment due to the operation of the fan in the microwave oven cavity; the value of h was determined by fitting the simulated temperature evolution to the experimental data to be around 40 W/m2  K.

,

ðE  E 1 Þ U E 1 R, , E1 U E1

ð15Þ

The Poynting theorem was used to evaluate the input microwave power by: Z ð16Þ P in ¼ S dA A

ð19Þ

The species balance equation that was used to describe the β-carotene concentration evolution in the extraction solvent is given as (Xiao et al., 2012): ( kβ1 ðC βmax  C β Þn ; T oT d ∂C β ¼ ð20Þ  kβ2 C m T ZT d ∂t β ;

∇C β ¼ 0 and nðk∇TÞ ¼ hðT T 1 Þ

At interfaces between solvent, glass and air:

ð17Þ

When the temperature of the solvent reached its boiling point (T b ), it was assumed that the entire heat from the microwave energy was used to evaporate the solvent; nevertheless, the boiling effect was not considered any further in order to simplify the model. For this reason, the temperature of the solvent was limited to a maximum value of T b and the energy equation becomes (Budd and Hill, 2011): ( ∇ Uðk∇TÞ þ q‴; T o T b ∂T ρC p ¼ ð18Þ 0; T ¼ Tb ∂t

At t ¼ 0 : C β ¼ C β0 and T ¼ T 0 Boundary conditions: At microwave cavity and waveguide walls: nH ¼ 0

445

3.3. Thermal and dielectric properties of extraction solvent The thermal and dielectric properties of each component of the solvent system were assumed to depend on the solvent temperature and could be described by the following equations: k ¼ C 1 þC 2 T þ C 3 T 2 þC 4 T 3

ð23Þ

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C p ¼ ðC 1 þ C 2 T þ C 3 T 2 þ C 4 T 3 Þ=ðM:W:Þ ½1 þ ð1  T=C 3 ÞC 4 

ρ ¼ ðC 1 =C 2

3.5. Model implementation

ð24Þ

Þ U ðM:W:Þ

The above model was solved using COMSOL MultiphysicsTM version 3.5 (Comsol AB, Stockholm, Sweden) with the direct solver (UMFPACK) linear system, which is the default solver for solving unsymmetric sparse linear systems in finite element problems (Datta and Rakesh, 2010).

ð25Þ

ε0 ¼ C 1 þC 2 T þ C 3 T 2 þC 4 T 3

ð26Þ

ε″ ¼ C 1 þ C 2 T þ C 3 T 2 þ C 4 T 3

ð27Þ

where M:W: is the molecular weight of each pure component. The molecular weights of acetone, ethanol, and hexane are 58.079, 46.068, and 86.175 g/mol, respectively. The constants (C 1 , C 2 , C 3 , and C 4 ) of each component and each property are listed in Table 2.

4. Results and discussion 4.1. Mesh independence test Mesh independence test was performed to ensure that the simulated variables were not affected by the mesh density. Although only the evolutions of the volume-average mixture (sample and extraction solvent) temperature and β-carotene concentration are reported, these evolutions were derived from the spatial distributions of the temperature and concentration and hence were affected by the mesh density. The number of tetrahedral elements was varied until it did not affect the evolution of the mixture temperature; the number of elements was varied from 2249 to 9054. The evolutions of the simulated volume-average mixture temperature when using different numbers of elements are shown in Fig. 3. Since the evolutions of the mixture temperature obtained when using 5454 and 9054 elements were quite similar, 5454 tetrahedral elements were selected for all the subsequent simulations. The final mesh characteristics are shown in Fig. 4.

3.4. Intermittent MAE When the intermittent MAE was conducted, the electric field E is given by: ( E; τn r t r τðn þ αÞ E¼ ð28Þ 0; τðn þ αÞ r t r τðn þ1Þ where τ is the overall cycle period, n is the number of MW irradiation cycle (n ¼ 0, 1, 2) and α is the intermittency ratio, which is defined as the fraction of a cycle when microwave irradiation was on: α¼

τon τon ¼ τ τon þ τoff

ð29Þ

During an ‘on’ period, the energy and species balance equations are the same as those during the continuous MAE (Eqs. (18) and (20)). However, during an ‘off’ period, the energy and species balance equation are as follows: ∂T ¼ ∇ Uðk∇TÞ ∂t ( kβoff1 ðC βmax C β Þn ; ∂C β ¼  kβoff 2 C m ∂t β ;

ρcp

4.2. Mixture temperature evolution Firstly, the absorbed microwave power needed to be numerically estimated since the solvent could not absorb all the supplied microwave energy. It was found that the set microwave powers of 180 and 300 W were equivalent to the absorbed powers of 50 and 100 W, respectively. The specific absorbed microwave powers corresponding to Conditions 1 and 5; 2 and 6; 3 and 7; as well as 4 and 8 were 0.92, 0.46, 1.85 and 0.92 W/g solvent, respectively. The simulated mixture temperature evolutions at various conditions were compared with the experimental data for the continuous MAE as shown in Fig. 5a–d. The spatial distributions of the

ð30Þ T oTd

ð31Þ

T ZTd

The initial and boundary conditions are similar to those in the case of the continuous MAE (Eqs. (21) and (22)). Table 2 Constant values in Eqs. (23)–(27). C1 Thermal conductivity (k) Acetone Ethanol Hexane Heat capacity (cp) Acetone Ethanol Hexane Density (ρ) Acetone Ethanol Hexane Dielectric constant (ε0 ) Acetone Ethanol Hexane Dielectric loss factor (ε″) Acetone Ethanol Hexane

C2

0.2878 0.2468 0.2249 135,600 102,640 172,120

C3

 0.0004  0.0003  0.0004  177.00  139.63  183.78

C4

0 0 0

Reference

0 0 0

Green and Perry (2008) Green and Perry (2008) Green and Perry (2008)

0.2837  0.0303 0.8873

0.0007 0.0020 0.0000

Green and Perry (2008) Green and Perry (2008) Green and Perry (2008)

0.2913 0.2318 0.2754

Green and Perry (2008) Green and Perry (2008) Green and Perry (2008)

1.2332 1.6288 0.7082

0.2589 0.2747 0.2641

508.2000 514.0000 507.6000

53.6070 1444.1000 2.3202

 0.1097  14.7750  0.0015

0 0.0500 0

0  5.5556  10  5 0

Price (1969) Zhao and Nikawa (2011) Mopsik (1967)

5.4337  1576.9000 0.0005

 0.0147 13.9590 0.0000

0 0.0406 0

0 3.8889  10  5 0

Punt (1997) Zhao and Nikawa (2011) Chen and Spiro (1994)

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

65.00 60.00

Temperature (°C)

55.00 50.00 45.00 9054 elements

40.00

5454 elements 35.00

3141 elements 2264 elements

30.00

2249 elements 25.00

0

1

2

3

4

5

6

7

Time (min) Fig. 3. Evolutions of mixture temperature at different numbers of elements.

447

In the case of the intermittent MAE, the experimental conditions were similar to those of the continuous MAE as mentioned earlier. However, the microwave energy was supplied as a cycle with ‘on’ and ‘off’ periods. The intermittency ratio (α) was fixed at 0.25. The information on each on/off/on period at different conditions is given in Table 1. The simulated temperature evolutions were compared with the experimental data as shown in Fig. 6a–d. The temperature changed along with the ‘on’ and ‘off’ periods, as expected. In general, the trend of the simulated results was quite similar to that of the experimental data with the R2 in the range of 0.87–0.89 in the cases of Conditions 5, 7 and 8 (Fig. 6a,c,d), indicating that the model could be adequately used to predict the evolution of the mixture temperature during the intermittent MAE. During the first ‘on’ period, the temperature evolution was similar to that of the continuous MAE. However, in the case of Condition 6 (Fig. 6b), during the second ‘on’ period, the results obtained from the model and the experiment were quite different. This is probably due to the earlier boiling of some components (hexane and acetone) of the extraction solvent mentioned earlier. 4.3. β-Carotene concentration evolution

Fig. 4. Mesh characteristics of the simulated MAE system.

temperature were first simulated and their volume-average values were compared with the experimental data. Note that although the model could be used to predict the spatial distributions of the electromagnetic field as well as the temperature of the mixture, it was not possible to compare these distributions with the experimental data since only one fiber-optic thermometer was available and used to measure the mixture temperature at a specific location. Since in reality natural convection did exist and caused the mixture to flow and mix, the simulated volume-average (instead of values at a specific fixed location) temperature should be reasonably comparable with the experimental data. The same limitation and hence the validation approach applied in the case of the β-carotene concentration, which could not also be measured locally. The volume-average concentration values, which were obtained from the simulated spatial distributions of the β-carotene concentration, were compared with the experimental data (Section 4.3). It can be seen that the model could be used to predict the temperature evolutions quite adequately with the R2 in the range of 0.92–0.99. Nevertheless, as is seen in Fig. 5b, the trend of the experimental data was not similar to those of the others. At that condition (Condition 2) the system containing a large amount of solvent was subject to a lower level of microwave power. This implies that it would take rather long for the mixture component with a lower boiling point (acetone) to completely evaporate and hence a longer period of relatively constant temperature. The model nevertheless did not consider each solvent component individually; therefore, the simulated temperature kept increasing until reaching the boiling temperature of the whole solvent system, which was measured to be around 58 1C.

In the case of the continuous MAE, the species balance equation required 4 empirical parameters that had to be determined, which are n, m, kβ1 and kβ2 . The values of these parameters were estimated by adjusting the β-carotene concentration evolution in the model results to the experimental data at each condition. The maximum β-carotene concentrations, on the other hand, were obtained from Soxhlet extraction experiments and were noted to be 171.88 and 183.69 mg/100 g dry basis when the solvent volumes were 75 and 150 mL, respectively. It was found that the order of the extraction rate (n) and the order of the degradation rate (m) in Eq. (20) were equal to unity. The extraction rate constant (kβ1 ) and degradation rate constant (kβ2 ) were noted to be a function of the specific absorbed microwave power (P0 ) in W/g solvent as well as of the sample to solvent mass ratio (R0 ) in g carrot peels/g solvent. The relation between the rate constants and both ratios can be described by a simple polynomial expression as Eq. (32). The extraction rate constant (kβ1 ) and degradation rate constant (kβ2 ) were input to the models on the left hand side of Eq. (32). The parameters a, b, c and d were estimated by adjusting the estimated β-carotene concentration evolution to match the experimental data at each condition. The values of these constants are given in Table 3. kβi ¼ a þ bP 0 þ cR0 þ dP 02

ð32Þ

Comparison between β-carotene concentrations from the model and the experiments is illustrated in Fig. 7a–d. It can be seen that the model could again be used to represent the β-carotene concentration evolution quite adequately. The β-carotene concentration tended to increase until the volume-average temperature of the mixture reached around 55 1C (see Fig. 5a–d) before starting to decrease. In Condition (2), however, the simulated β-carotene concentration evolution was quite different from the experimental data. This occurred possibly because the simulated temperature during the early period of extraction (Fig. 5b) was lower than the experimental temperature. This therefore resulted in the simulated β-carotene concentration being higher than the experimental concentration because the mixture had the average temperature lower than the degradation temperature of β-carotene. On the other hand, the simulated temperature evolution was higher than the experimental temperature during the later period. The simulated β-carotene concentration was thus lower than the experimental concentration because the mixture had the simulated volume-average temperature higher than the degradation temperature of β-carotene.

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

70

70

60

60 Temperature (°C)

Temperature (°C)

448

50 40 30 20

1

2

3

4

5

40 30

Experiment Simulation 0

50

20

6

Experiment Simulation 0

2

4

70

70

60

60

50 40 30 20

0.5

1

1.5

8

10

2

2.5

50 40 30

Experiment Simulation 0

6

Time (min)

Temperature (°C)

Temperature (°C)

Time (min)

20

3

Experiment Simulation 0

1

2

Time (min)

3

4

5

Time (min)

70

90

60

80

50

70

Experiment Simulation

Temperature (°C)

Temperature (°C)

Fig. 5. Comparison between simulated and experimental mixture temperature evolutions for continuous MAE: (a) Condition 1; (b) Condition 2; (c) Condition 3; and (d) Condition 4.

40 30 20 Experiment 10 0

5

10

15

50 40 30

Simulation 0

60

20

20

0

10

20

65

70

60

65

55

60

50

55

45 40 35 30

Experiment

25

Simulation

20

0

2

4

Time (min)

40

Time (min)

Temperature (°C)

Temperature (°C)

Time (min)

30

6

50 45 40 35 30

Experiment Simulation

25 8

20

0

5

10

15

Time (min)

Fig. 6. Comparison between simulated and experimental mixture temperature evolutions for intermittent MAE: (a) Condition 5; (b) Condition 6; (c) Condition 7; and (d) Condition 8.

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

In the case of the intermittent MAE, the species balance equation required 8 empirical parameters, which are n, m, kβ on 1 , kβ on 2 ,kβ off 1 , kβ off 2 , kβ on 3 and kβ on 4 . The values of these parameters were estimated by adjusting the estimated β-carotene concentration evolution results to the experimental data in each period (‘on’ and ‘off’) at each condition. As an example, only the values at α ¼0.25 were fitted and are shown here. It was found that the order of the extraction rate (n) and the order of the degradation rate (m) in Eq. (20) (for ‘on’ period) and in Eq. (31) (for ‘off’ period) were again equal to unity. The extraction rate constant (kβ on 1 ) and degradation rate constant (kβ on 2 ) of the first ‘on’ period, the extraction rate constant (kβ off 1 ) and degradation rate constant (kβ off 2 ) of the ‘off’ period and the extraction rate constant (kβ on 3 ) and degradation rate constant (kβ on 4 ) of the second ‘on’ period also depended on R0 . The relationship between the above rate constants and P0 and R0 could also be described as: kβj ¼ e þ f P 0 þ gR0 þhP 02

ð33Þ

where e, f, g and h are constants of each rate constant for the intermittent MAE, which are given in Table 4. The simulated and experimental evolutions of the β-carotene concentration are illustrated in Fig. 8a–d. It is seen that the simulated β-carotene concentration evolutions agreed with the experimental data quite adequately with the R2 in the range of 0.84–0.92. The

β-carotene concentration increased quite rapidly during the first ‘on’ period. However, towards the end of the ‘on’ period, the β-carotene concentration started to decrease because the mixture temperature had reached the degradation temperature of β-carotene (55 1C). The concentration then increased again but at a lower rate (or, in other words, with lower extraction rate constant) during the ‘off’ period because there was no microwave energy to assist the extraction; the transport of β-carotene from carrot peels into the extraction solvent nevertheless took place in much the same manner as that in the case of a extraction situation. The mixture temperature was also obviously lower, resulting expectedly to lower degradation of β-carotene. After turning on the microwave radiation again, the β-carotene content started to decrease due to the higher temperature of the mixture and hence more degradation. The highest β-carotene concentration occurred before the second ‘on’ period for all conditions except Condition 6 whose first ‘on’ period was longer than that of the other conditions. Because of this reason, more than 60% of β-carotene content in the carrot peels was extracted during the first ‘on’ period. Comparing with the yields achievable via Soxhlet extraction, the maximum yields of MAE when operated in continuous and intermittent modes were lower by around 30% and 20%, respectively. Through careful optimization using the results simulated Table 4 Constants for rate constants at α ¼ 1/4 in Eq. (33). j

Table 3 Constants for rate constants in Eq. (32). i

a

b

c

d

1 2

 0.003924  0.002999

0.018317 0.008533

0.093675 0.101461

 0.006944  0.003926

120 100 80 60 40 0

2

4

6

1 2 1 2 3 4

e

f

g

h

 0.008652  0.009129  0.003206  0.001634  0.005554  0.003695

0.042194 0.030656 0.015171 0.006319 0.026258 0.022637

 0.280905  0.140708  0.192488 0.140700  0.324630  0.217455

 0.015553  0.011902  0.004787  0.003127  0.009536  0.007192

Experiment Simulation

140 β-carotene concentration (mg/100g dry basis)

β-carotene concentration (mg/100g dry basis)

On On Off Off On On

Experiment Simulation

140

120 100 80 60 40

8

0

2

4

Time (min)

β-carotene concentration (mg/100g dry basis)

β-carotene concentration (mg/100g dry basis)

120 100 80 60

1

2

3 Time (min)

8

10

4

5

Experiment Simulation

140

Experiment Simulation

0

6

Time (min)

140

40

449

6

120 100 80 60 40

0

1

2

3

4

5

6

Time (min)

Fig. 7. Comparison between simulated and experimental β-carotene concentration evolutions for continuous MAE: (a) Condition 1; (b) Condition 2; (c) Condition 3; and (d) Condition 4.

450

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

140 β-carotene concentration (mg/100g dry basis)

β-carotene concentration (mg/100g dry basis)

140 120 100 80 60

Experiment Simulation

120 100 80 60

Experiment Simulation

40

40 0

5

10

15

20

0

10

20

Time (min)

40

140 β-carotene concentration (mg/100g dry basis)

β-carotene concentration (mg/100g dry basis)

140 120 100 80 60 40

30

Time (min)

Experiment Simulation

120 100 80 60

Experiment Simulation

40 0

2

4

6

8

0

5

10

15

Time (min)

Time (min)

Fig. 8. Comparison between simulated and experimental β-carotene concentration evolutions for intermittent MAE: (a) Condition 5; (b) Condition 6; (c) Condition 7; and (d) Condition 8.

from the present model, however, the yield achievable via MAE may be enhanced. The model should also allow a better design of the system and its operation since detailed parametric study of the process can now be performed.

5. Conclusions A mathematical model that can be used to describe the evolutions of the temperature and concentration of an extracted compound in a solvent during MAE was proposed. For the continuous MAE, the results from the models showed that the model was able to represent the temperature and β-carotene concentration evolutions quite adequately. In a specific case, however, the model could not capture the trend of the temperature evolution since evaporation of the solvent was not considered in the model. The intermittent MAE was also simulated with the microwave energy supplied as a cycle at an intermittency ratio of 0.25. The trends of the estimated temperature and β-carotene concentration evolutions were similar to those of the experiments. During the first ‘on’ period, the temperature evolutions were similar to those of the continuous MAE. Again, however, during the second ‘on’ period of a specific case, the results obtained from the model and experiment were quite different. This is again probably due to the earlier boiling of the extraction solvent, which was not taken into account in the model. A future model should therefore include a phase change equation in order to enhance the accuracy of the temperature evolution prediction. Moreover, the amount of carrot peels may be considered in the model and the species balance equation should include the diffusion term to allow a more realistic simulation. Optimization of the intermittent MAE process via such technique as response surface methodology using the results simulated from the present model may also be attempted to obtain the optimized extraction condition.

Nomenclature A B cp Cβ Cβmax D f E H h J j k kβ1 kβ2 n m Pin q q‴ S T t

cross sectional area of microwave waveguide (m2) magnetic flux density (Wb/m2) specific heat capacity (J/(kg  K)) concentration of β-carotene (mg/100 g dry basis) maximum concentration of β-carotene (mg/100 g dry basis) flux density (C/m2) microwave frequency (fixed at 2.45 GHz) electric field (V/m) magnetic field (A/m) convective heat transfer coefficient (W/m2  K) current density (A/m2) imaginary unit thermal conductivity (W/m  K) extraction rate constant (1/(s  (mg/100 g dry basis)(n  1))) degradation rate constant (1/(s  (mg/100 g dry basis)(n  1))) order of extraction rate order of degradation rate input microwave power (W) electric charge density (C/m3) volumetric heat generation rate Poynting vector (W/m2) temperature (K) time (s)

Greek symbols ε0 εr ε0 ε″

vacuum permittivity (8.8542  10  12 F/m) relative permittivity dielectric constant dielectric loss factor

N. Chumnanpaisont et al. / Chemical Engineering Science 116 (2014) 442–451

μ0 μr ρ

s

ω tan δ

vacuum permeability (H/m) (4π  10  7 N/A) relative magnetic permeability solvent density (kg/m3) electric conductivity (S/m) angular velocity (rad/s) dielectric loss coefficient

Acknowledgments The authors express their sincere appreciation to the Thailand Research Fund (TRF) for supporting the study financially. References Amarni, F., Kadi, H., 2010. Kinetics study of microwave-assisted solvent extraction of oil from olive cake using hexane: Comparison with the conventional extraction. Innov. Food Sci. Emerg. Technol. 11, 322–327. Bagherian, H., Ashtiani, F.Z., Fouladitajar, A., Mohtashamy, M., 2011. Comparisons between conventional, microwave- and ultrasound-assisted methods for extraction of pectin from grapefruit. Chem. Eng. Process.: Process Intensif. 50, 1237–1243. Budd, C.J., Hill, A.D.C., 2011. A comparison of models and methods for simulating the microwave heating of moist foodstuffs. Int. J. Heat Mass Transfer 54, 807–817. Chan, C.H., Yusoff, R., Ngoh, G.C., 2013. Modeling and prediction of extraction profile for microwave-assisted extraction based on absorbed microwave energy. Food Chem. 140, 147–153. Chandrasekaran, S., Ramanathan, S., Basak, T., 2013. Microwave food processing A review. Food Res. Int. 52, 243–261. Chen, S.S., Spiro, M., 1994. Study of microwave extraction of essential oil constituents from plant materials. J. Microw. Power Electromagn. Energy 29, 231–241. Datta, A., Rakesh, V., 2010. An Introduction to Modeling of Transport Processes: Applications to Biomedical Systems. Cambridge University Press, New York. Fulzele, D.P., Satdive, R.K., 2005. Comparison of techniques for the extraction of the anti-cancer drug camptothecin from Nothapodytes foetida. J. Chromatogr. A 1063, 9–13. Geedipalli, S., Datta, A.K., Rakesh, V., 2008. Heat transfer in a combination microwave-jet impingement oven. Food Bioprod. Process. 86, 53–63. Goula, A.M., Adamopoulos, K.G., 2010. Kinetic models of β-carotene degradation during air drying of carrots. Dry. Technol. 28, 752–761. Hemwimon, S., Pavasant, P., Shotipruk, A., 2007. Microwave-assisted extraction of antioxidative anthraquinones from roots of Morinda citrifolia. Sep. Purif. Technol. 54, 44–50.

451

Hiranvarachat, B., Devahastin, S., Chiewchan, N., Raghavan, G.S.V., 2013. Structural modification by different pretreatment methods to enhance microwaveassisted extraction of β-carotene from carrots. J. Food Eng. 115, 190–197. Hiranvarachat, B., Devahastin, S., 2014. Enhancement of microwave-assisted extraction via intermittent radiation: Extraction of carotenoids from carrot peels. J. Food Eng. 126, 17–26. Jian, Y., Yang, X.Q., Huang, K.M., 2010. Numerical analysis of the influence of stir on water during microwave heating. Prog. Electromagn. Res. C 17, 105–119. Maran, J.P., Sivakumar, V., Thirugnanasambandham, K., Sridhar, R., 2014. Microwave assisted extraction of pectin from waste Citrullus lanatus fruit rinds. Carbohydr. Polym. 101, 786–791. Kiss, G.A.C., Forgacs, E., Serati, T.C., Mota, T., Morais, H., Ramos, A., 2000. Optimisation of the microwave-assisted extraction of pigments from paprika (Capsicum annum L.) powders. J. Chromatogr. A 889, 41–49. Mopsik, F.I., 1967. Dielectric constant of n-hexane as a function of temperature, pressure and density. J. Res. Natl. Bur. Stand. A: Phys. Chem. 71A, 287–292. Navarrete, A., Mato, R.B., Cocero, M.J., 2012. A predictive approach in modeling and simulation of heat and mass transfer during microwave heating. Application to SFME of essential oil of Lavandin Super. Chem. Eng. Sci. 68, 192–201. Pan, X., Niu, G., Liu, H., 2003. Microwave-assisted extraction of tea polyphenols and tea caffeine from green tea leaves. Chem. Eng. Process.: Process Intensif. 42, 129–133. Pozar, D., 2005. Microwave engineering, 3rd edition Wiley, New York. Green, D.W., Perry, R.H. (Eds.), 2008. Perry's Chemical Engineers' Handbook, 8th edition McGraw-Hill, New York. Price, A.H., 1969. The permittivity of liquids. In: Sugden, T.M. (Ed.), Dielectric Properties and Molecular Behaviour. Butler Tanner & Dennis, Frome. Punt, M.M., 1997. Microwave-enhanced Extraction of Organic Contaminants from Soil (M.Sc. thesis)Department of Agricultural and Biosystems Engineering, McGill University, Montreal, Canada. Sinha, K., Chowdhury, S., Saha, P.D., Datta, S., 2013. Modeling of microwave-assisted extraction of natural dye from seeds of Bixa orellana (annatto) using response surface methodology (RSM) and artificial neural network (ANN). Ind. Crops Prod. 41, 165–171. Spigno, G., DeFaveri, D.M., 2009. Microwave-assisted extraction of tea phenols: A phenomenological study. J. Food Eng. 93, 210–217. Wang, J., Zhang, J., Zhao, B., Wang, X., Wu, Y., Yao, J., 2010. A comparison study on microwave-assisted extraction of Potentilla anserina L. polysaccharides with conventional method: molecule weight and antioxidant activities evaluation. Carbohydr. Polym. 80, 84–93. Wang, Z, Ding, L., Li, T., Zhou, X., Wang, L., Zhang, H., Liu, L., Li, Y., Liu, Z., Wang, H., Zeng, H., He, H., 2006. Improved solvent free microwave extraction of essential oil from dried Cuminum cyminum L. and Zanthoxylum bungeanum Maxim. J. Chromatogr. A 1102, 11–17. Xiao, X., Song, W., Wang, J., Li, G., 2012. Microwave-assisted extraction performed in low temperature and in vacuo for extraction of labile compounds in food samples. Anal. Chim. Acta 712, 85–93. Zhao, K., Nikawa, Y., 2011. Temperature evaluation of complex permittivity in microwave material. Pac. Sci. Rev. 12, 263–268.